Directions: Please show all work and be as neat as
possible. Please put your answers in the provided boxes.
6 points
1. For the quadratic function f (x) = x2-3x-28, find
a) the x- intercepts , and
b) the y-intercept.
x-intercepts: (-4,0) and (7,0)
y-intercept: (0,-28)
7 points
2. Identify the equations .html">vertex of the quadratic function f (x) =
7x2-28x+58.
Vertex: (2,30)
7 points
3. Formulas /solving-quadratic-equations-4.html">Solve the inequality x2-17x≥60. Give your answer in
interval notation.
7 points
4. De termine if x -5 is a factor of f (x) = x3 -8x2
-55x+350. If x-5 is a factor of the polynomial then factor
the polynomial completely.
Is x-5 a factor? Yes
If so the factorization is x3+4x2-31x-70 = (x-5)
(x-10)(x+7)
7 points
5. Factor the polynomial f (x) = 6x2+19x-7 completely
7 points
6. Factor the polynomial f (x) = x2-13x+36 completely.
7 points
7. Find a polynomial with real coefficients that has the
zeros 6 and 3+i.
6 points
8. List all possible rational zeros of f (x) =
14x3-65x2-26x+5 using the rational zero test .
7 points
9. Find all real zeros of the function f (x) =
x9-24x8+144x7. Give the multiplicity of each repeated zero.
x = 0 is a zero of multiplicity 7
x = 12 is a zero of multiplicity 2
6 points
10. Use the Leading Coefficient Test to determine the
extreme right-hand and left-hand behavior for the graph of
f (x) = -4x7+63x4-3x2+1. Demonstrate this behavior with a picture.
7 points
11. Find the domain of the rational function
Give the answer in interval notation.
7 points
12. For the rational function
find
a) the x-intercepts, and
b) the y-intercept.
6 points
13. Find any vertical asymptotes of the rational function
6 points
14. Find the horizontal asymptote of the rational function
7 points
15. Find the oblique asymptote of the rational function
Formulas
